An example of seismic time picking by third‐order bicoherence

Abstract

Conventional seismic time‐delay estimation relies on the crosscorrelation that quantifies the similarities between two measurements in the second‐order time domain. When the noise correlation in the measurements is considerable, the correlation peak can be substantially distorted, resulting in imprecise and even biased estimation of the time delay. The synthetic data computed by Ikelle et al. (1993) and Ikelle and Yung (1994) in their studies of wave propagation through random media provide a good example of data with considerable noise correlation. In picking the arrival times in this data set, we found that the crosscorrelation technique suffers both from the severely restricted signal bandwidth and from the presence of coda. Here we present an alternative approach involving high‐resolution nonparametric time‐delay estimation in the third‐order domain.

Methods for Improving Seismic Event Location Processing

“…In both cases the lower trace (the stacked signal obtained by shifting the waveform of the first event with bispectrum-determined lags) has a larger root-mean-square (RMS) amplitude than the upper trace, which is obtained after shifting the waveform of the first event with the CC-determined lags. The above example corroborates the findings of Nikias and Pan (1988) and Yung and Ikelle (1997) that the bispectrum method works better than CC techniques in getting relative time delay between two similar signals contaminated by correlated noise.…”

“…In both cases the lower trace (the stacked signal obtained by shifting the waveform of the first event with bispectrum-determined lags) has a larger root-mean-square (RMS) amplitude than the upper trace, which is obtained after shifting the waveform of the first event with the CC-determined lags. The above example corroborates the findings of Nikias and Pan (1988) and Yung and Ikelle (1997) that the bispectrum method works better than CC techniques in getting relative time delay between two similar signals contaminated by correlated noise.In our approach, we compute two more time delay estimates between the waveform pairs with the bispectrum method (the raw data and band-pass filtered data) and use them to verify the WCC-determined one using the bandpass filtered data. This technique can provide quality control over the selected time delay estimates and potentially provide more differential travel time data for close events pairs, by verifying the reliability of differential times that might not meet the threshold criterion.…”

“…When the underlying signal inside two similar time series can be regarded as a non-Gaussian process and the noise sources as zero-mean Gaussian processes, the similarities between the two time series can be better compared in the third-order or bispectrum domain (Nikias and Raghuveer, 1987;Nikias and Pan, 1988;Yung and Ikelle, 1997). This bispectrum method takes advantage of the fact that for Gaussian processes only all spectra of order higher than two are identically zero.…”

Performance of time-delay estimators

“…The hypothesis of Knapp and Carter (1976) that signal and additive noise are jointly stationary Gaussian processes that are essential to derive an analytical expression for the estimator, as well as the other hypothesis of additive and spatially uncorrelated noise, may not be verified in seismic exploration. Methods based on higher-order statistics (Mendel, 1991), for instance, which have been used to track first arrivals (Yung and Ikelle, 1997) can eliminate the cross-spectrum that arises in the presence of correlated Gaussian noise. However, higher-order statistics are difficult to estimate for the relatively short time series of seismic data.…”

Seismic $P$ Phase Picking Using a Kurtosis-Based Criterion in the Stationary Wavelet Domain

“…Over the last two decades, numerous algorithms have been developed for P arrival identification based on energy analysis [1]- [5], polarization analysis [6]- [10], artificial neural networks [11], [12], maximum likelihood methods [13], [14], fuzzy logic theory [15], autoregressive techniques [16]- [19], higher-order statistics [20]- [24], sample of a sequence.…”